Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance

TLDR

By prescribed performance we mean that the tracking error should converge to an arbitrarily small residual set, with a convergence rate no less than a prespecified value, and a maximum overshoot less than a sufficiently small prespecified constant. The paper develops a novel robust adaptive controller for multi‑input multi‑output feedback linearizable nonlinear systems with unknown nonlinearities to guarantee prescribed performance. The key mechanism is to view the prescribed performance constraints as tracking error bounds and transform the constrained system into an equivalent unconstrained one via an appropriately defined output error transformation. The controller achieves uniform ultimate boundedness of the transformed output error, boundedness of all closed‑loop signals, smoothness with easily chosen parameters, bypasses loss of controllability, and simulation on a two‑link robot confirms the approach.

Abstract

A novel robust adaptive controller for multi-input multi-output (MIMO) feedback linearizable nonlinear systems possessing unknown nonlinearities, capable of guaranteeing a prescribed performance, is developed in this paper. By prescribed performance we mean that the tracking error should converge to an arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. Visualizing the prescribed performance characteristics as tracking error constraints, the key idea is to transform the ldquoconstrainedrdquo system into an equivalent ldquounconstrainedrdquo one, via an appropriately defined output error transformation. It is shown that stabilization of the ldquounconstrainedrdquo system is sufficient to solve the stated problem. Besides guaranteeing a uniform ultimate boundedness property for the transformed output error and the uniform boundedness for all other signals in the closed loop, the proposed robust adaptive controller is smooth with easily selected parameter values and successfully bypasses the loss of controllability issue. Simulation results on a two-link robot, clarify and verify the approach.